   Chapter 13, Problem 78GQ

Chapter
Section
Textbook Problem

A solution is 4.00% (by mass) maltose and 96.00% water. It freezes at −0.229 °C. (a) Calculate the molar mass of maltose (which is not an ionic compound). (b) The density of the solution is 1.014 g/mL Calculate the osmotic pressure of the solution.

(a)

Interpretation Introduction

Interpretation: The molar mass of maltose solution has to be determined.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Change in freezing point is calculated by using the equation,

ΔTfp=Kfpmsolute

where,

Kfp is the molal freezing point depression constant.

Osmotic pressure: The pressure created by the column of solution for the system at equilibrium is a measure of the osmotic pressure.

π=icRT

where,

c is the molar concentration

i is the van’t Hoff factor

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Density is calculated by the equation,

Density=massvolume

Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.

Molarity (M) =Numberofmolesofsolute1literofsolution

Explanation

Given,

ΔT=0.2290C

Mass of maltose is 4g

Mass of water is 96g=0.096kg

Molal freezing point depression constant of water is 1.860C/m

Change in freezing point is calculated by using the equation,

ΔTmp=Kmpmsolute

Hence,

The concentration is calculated by,

Concentration,msolute=ΔTmpKmp=(0.2290C0C)(1.860C/m)=0

(b)

Interpretation Introduction

Interpretation: The osmotic pressure of the maltose solution has to be determined.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Osmotic pressure: The pressure created by the column of solution for the system at equilibrium is a measure of the osmotic pressure.

π=icRT

where,

c is the molar concentration

i is the van’t Hoff factor

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Density is calculated by the equation,

Density=massvolume

Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.

Molarity (M) =Numberofmolesofsolute1literofsolution

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